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Discrete Math and Analyzing Social Graphs
Week 2
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1.

Question 1

What is the number of 5-card hands with four hearts and one spades?

1 / 1 point

9295

Correct

Exactly! It is $\binom{13}{4} \times \binom{13}{1} =9295$ .

2.

Question 2

What is the number of bit-strings (that is, strings consisting of 0's and 1's) of length 8 where the number of 0's is equal to the number of 1's?

For example, there are two such strings of length two: 01 and 10.

1 / 1 point

70

Correct

Exactly! We just need to select four (out of eight positions) of 0's.